Friends

Detailed Description

Iterators for skiplist can never be completely invalidated unless the element for that iterator is erased. If you insert or remove an element that is located before iterator X, you will need to call X.refresh() to revalidate the iterator. This will simply recalculate the index.

Certain iterator operations do not require the index (ie. do not require revalidation).
For SkipLists that use a key, all iterator comparisons are safe on invalidated iterators.
For SkipLists that don't use a key, less than comparisons (<,<=,>,>=) only work on validated iterators.
For SkipLists that use a key, all increment and decrement operations are safe on invalidated iterators.
For SkipLists that do not have a key and only have an index, incrementing is always safe on invalidated iterators.
For SkipLists that do not have a key and only have an index, decrementing is safe on invalidated iterators on lists that use reverse pointers. Invalidated iterators for IndexedSSkipList (note the extra S) cannot decrement without refreshing first.
Random access always requires a validated iterator.
Distance between two iterators always requires two validated iterators.
Accessing an element via an iterator is always safe.
Equality comparisons (==,!=) are always safe.

Asymptotic worst case performance are specified for each method. The following performances are possible.

O(1) Constant time.

O(logn) Logarithmic time.

O(n) Linear time.

Note that updating the list will always require from 1 to logn operations since there are between 1 to logn levels. In the performance specifications, updating all levels of the list for a single node is stated as O(1) since there will always be a small finite number of levels. Note that this does NOT include searching for the appropriate nodes to update at each level. This will always take O(logn) and is specified as such.

For example, removing a node from the front of the list will require logn operations, yet it is specified as O(1) because only a small finite amount of forward pointers need be updated which are readily available. But deleting in the middle of the list would require searching for the forward pointers that need updating and this would be indicated as O(logn).

It is up to the user to take these differences into account and use O(logn) OR O(1) as required when operations work on elements at the front or end of the list as well as any other time where all forward pointers are readily available. Also note that caching is enabled which will also speed up many operations.

The operations that are marked O(1), but take logn operations will be indicated as O(1C)

Attempts to locate an element with the same ordering as val. if it is not found, a new element initialized with val is inserte into the list. In either case, an iterator where is designated for the element. If an insertion occurred, pair(where,true) is returned. Otherwise, pair(where,false) is returned.